Weighted Multifractal Spectrum of V -Statistics

We analyze and describe the weighted multifractal spectrum of V-statistics. The description will be possible when the condition of “weighted saturation” is fulfilled. This means that the weighted topological entropy of the set of generic points of measure μ equals the measure-theoretic entropy of μ....

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Autores principales: Mesón, Alejandro Mario, Vericat, Fernando
Formato: Articulo
Lenguaje:Inglés
Publicado: 2020
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Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/132509
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Sumario:We analyze and describe the weighted multifractal spectrum of V-statistics. The description will be possible when the condition of “weighted saturation” is fulfilled. This means that the weighted topological entropy of the set of generic points of measure μ equals the measure-theoretic entropy of μ. Zhao et al. (J Dyn Differ Equ 30:937–955, 2018) proved that for any ergodic measure weighted saturation is verified, generalizing a result of Bowen. Here we prove that under a property of “weighted specification” the saturation holds for any measure. From this we obtain the description of the spectrum of V-statistics. This generalizes the variational result that Fan, Schmeling and Wu obtained for the non-weighted case.